Verified Answer :

LammettHash

\(\displaystyle\int\frac{\ln x^7}x\,\mathrm dx=7\int\frac{\ln x}x\,\mathrm dx\)

Set \(y=\ln x\), recalling that \(\mathrm dy=\dfrac{\mathrm dx}x\), so the integral is

\(\displaystyle7\int y\,\mathrm dy=\dfrac72y^2+C=\dfrac72(\ln x)^2+C\)

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